Hi again Rob
The bad news is that there is no service record for a likely Alfred (or Albert) Offord - nor indeed for any Offord in the 63rd Regt. (which at that time was 63rd. (the West Suffolk) Regiment of Foot).
The possible good news is that I think I could have identified this individual but this all depends on you getting the marriage certificate of Albert Offord and Eliza Neather - Staffordshire BMD site confirms that these 2 did marry each other but it was a civil marriage (not in a church) so no-one can look this up for you. If his father is shown as a Robert Offord then I believe I've found your man and can understand why his christian name has caused such confusion.
A Robert Offord (bc.1800 Westhorpe, Suffolk) married a Susanna Goold 24/5/1825 Thorpe Morieux, Suffolk and they had 4 children there:
ALBAN bp.15/1/1826
Robert bp.28/10/1827, bur.22/2/1829
Robert bp.11/4/1830
Samuel bp.5/5/1832, bur.9/5/1832
Susannah bc.1796 bur.21/8/1832 Thorpe Morieux.
Robert remarried to a Frances Tracey, widow on 9/6/1835 Brettenham, Suffolk and in 1841 they are in Brettenham with Alban (transcribed as Albion) and Robert junr.
Only Robert junr. is with them in 1851 and I cannot find Alban anywhere - I think this Alban could be the Albert (?) who married Eliza Neather in 1850 in Staffordshire. I don't think he can have been in the army for very long.
Alban Offord married in Lancashire in 1858:
Alban Offord, 32, widower, Police Man, son of Robert Offord, married Elizabeth Stubbs 22/9/1858 Horwich Chapel, Lancashire (per Lan-opc).
Bearing in mind that 'Alban' is missing in 1851 Census and that there is no earlier marriage in that name prior to 1858 I think that this is the guy who married Eliza Neather in 1850 and who were subsequently in Ireland in 1851. I suspect Eliza may have died in Ireland and that Alban returned to the UK and and took their child to her parents who subsequently raised him.
I won't start listing all the census details for Alban from 1861 in case I'm wrong but suffice to say that he's a Policeman (on Railway) 1861 In Roade, Northamptonshire, 1871 (Watchman) and 1881 (Brewers Labourer) at Burton upon Trent, Staffordshire. His death is recorded in Burton upon Trent in 1921 aged 95! He had at least 5 more children with his 2nd. wife.
Robert senior is living with Alban (transcribed as Allan) and family in 1881 so left Suffolk in his old age.
Everything hinges on the marriage certificate of 'Albert' Offord in 1850 and that it states his father as Robert.
Fingers crossed.
Annette